Linking Warm Dark Matter to Merger Tree Histories via Deep Learning Networks

TL;DR

This work demonstrates that graph neural networks trained on galaxy merger trees can infer Warm Dark Matter particle masses and select astrophysical feedback parameters from the DREAMS WDM simulation suite. By converting SubLink merger histories into graphs and employing a CosmoGraphNet–style architecture, the authors show strong WDM inference, achieving $R^2$ up to the high-0.9s when node features are rich (e.g., including $M_{\text{DM}}, M_{*}, M_{G}, \text{SFR}$), particularly for $M_{\text{WDM}} \lesssim 6$ keV. They also successfully recover $A_{\text{SN1}}$ and $A_{\text{SN2}}$ in favorable feature configurations, while $A_{\text{AGN}}$ remains largely unconstrained in MW-scale halos due to limited AGN activity. Analyses reveal that merger-tree abundance and DM halo mass carry the strongest WDM sensitivity, with temporal structure and baryonic content providing additional, context-dependent information. The work highlights both the promise and current limitations of using graph-based inference on merger histories to probe cosmology, offering a framework for extending such approaches to more realistic models and larger simulation suites.

Abstract

Dark matter (DM) halos form hierarchically in the Universe through a series of merger events. Cosmological simulations can represent this series of mergers as a graph-like ``tree'' structure. Previous work has shown these merger trees are sensitive to cosmology simulation parameters, but as DM structures, the outstanding question of their sensitivity to DM models remains unanswered. In this work, we investigate the feasibility of deep learning methods trained on merger trees to infer Warm Dark Matter (WDM) particles masses from the DREAMS simulation suite. We organize the merger trees from 1,024 zoom-in simulations into graphs with nodes representing the merger history of galaxies and edges denoting hereditary links. We vary the complexity of the node features included in the graphs ranging from a single node feature up through an array of several galactic properties (e.g., halo mass, star formation rate, etc.). We train a Graph Neural Network (GNN) to predict the WDM mass using the graph representation of the merger tree as input. We find that the GNN can predict the mass of the WDM particle ($R^2$ from 0.07 to 0.95), with success depending on the graph complexity and node features. We extend the same methods to supernovae and active galactic nuclei feedback parameters $A_\text{SN1}$, $A_\text{SN2}$, and $A_\text{AGN}$, successfully inferring the supernovae parameters. The GNN can even infer the WDM mass from merger tree histories without any node features, indicating that the structure of merger trees alone inherits information about the cosmological parameters of the simulations from which they form.

Figures (10)

• Figure 1: The graph representation of a merger tree from an example simulation within the DREAMS WDM MW zoom-in suite. The merger tree represents the merger history of a MW-mass subhalo beginning at $z=0$ (snapshot 90) and ending at $z=15$ (snapshot 0). All subhalos in the tree are included. The colors of the nodes, as well as the sizes of the nodes, represent the subhalo mass (ranging from $7 \times 10^{11}~\text{M}_\odot$ to $2.5 \times 10^{12} ~\text{M}_\odot$).
• Figure 2: A schematic diagram of the tree-to-graph conversion and the GNN architecture. Node features and edges (consisting of edge indices and meaningless edge features) are encoded into a graph, which then pass through several message passing layers and a final aggregation layer, producing an output prediction.
• Figure 3: The plotted results of training the four GNN models on merger trees with one node feature attached: subhalo snapshot number. Each plot shows the inferred parameter values versus the true parameter values. The parameter inferred is labeled at the bottom right of each plot. The keys at the top left of each plot refer to the node feature that was used in training the model to produce the plot (see Section \ref{['sec:node features']} for details). The dotted lines spanning the diagonals are where perfectly accurate predictions would fall. The inference of the WDM parameter is successful, particularly for lower masses, with a $R^2$ value of 0.708 and a RMSE of 0.082, as well as the SN1 parameter, with a $R^2$ value of 0.648 and a RMSE of 0.214. However, the $A_\text{SN2}$ and $A_\text{AGN}$ models both fail to make accurate predictions, as they only predict the mean value.
• Figure 4: The plotted results of training the WDM GNN on four different combinations of node features from the merger trees. Each plot shows the inferred WDM particle mass versus the true WDM particle mass. The keys at the top left of each plot refer to the node features that were used in training the model to produce the plot (see Section \ref{['sec:node features']} for details). The dotted line spanning the diagonals are where perfectly accurate predictions would fall. The model successfully infers the WDM particle mass for all of the node combinations, performing roughly the same for each combination of node features. The best performance, in the bottom right, has a $R^2$ value of 0.957 and a RMSE of 0.031, demonstrating highly accurate predictions.
• Figure 5: The plotted results of the best-performing node feature combinations from the $A_\text{SN1}$, $A_\text{SN2}$, and $A_\text{AGN}$ GNN models. Each plot shows the inferred parameter value versus the true parameter value in logspace. The dotted line spanning the diagonal is where perfectly accurate predictions would fall. In the top left of each plot, we show the node features used, and in the bottom right of each plot we show the parameter inferred by the model. The $A_\text{SN1}$ and $A_\text{SN2}$ models are successful ($R^2$ of 0.987 and $R^2$ of 0.880, respectively), and the $A_\text{AGN}$ model is unsuccessful ($R^2$ of 0.102).